Compton scattering from bound electrons: comparisons of the impulse approximation with exact IPA calculation

Abstract

The doubly differential cross section for Compton scattering from K-shell atomic electrons is calculated in the relativistic impulse approximation (lA) and compared with an exact relativistic second order S-matrix calculation based on the independent particle approximation (IPA). Comparison is made for several atoms and for incident photon energies up to 320 keV. A new criterion for the validity of the impulse approximation is given in terms of the average electron momentum contributing to the scattered photon spectrum rather than the momentum expectation value of the orbital electron. In the energy range considered here the impulse approximation gives a good description of the portion of the spectrum in which the new criterion is fulfilled.